The goddess Astarte
Like the Roman goddess Venus or the Greek goddess Aphrodite, Astarte started out as the goddess of the evening star. (And soon West Asian astronomers realized that the evening star is really the planet Venus.)
So Astarte is a lot like Aphrodite and Venus in many ways. Indeed, the Greek goddess Aphrodite may have originally been a version of the Phoenician Astarte.
Astarte as the wife of Baal
People worshipped Astarte mainly among the Phoenicians, and especially on the island of Cyprus.
But her worshippers thought of her a little differently in the Eastern Mediterranean. Here people thought of Astarte as the wife of Baal, the main Phoenician and Canaanite god. Probably early Jews also worshipped Astarte and Baal along with Yahweh. They sometimes thought of Yahweh as a brother of Baal.
Astarte and Ishtar
Christianity and Astarte
All through the Hellenistic and Roman periods in West Asia people kept on worshipping Astarte. People probably worshipped Astarte in Sassanian Iran, too. But when most people converted to Christianity and Buddhism in the 400s AD, they stopped thinking about Astarte so much.
Ancient Mesopotamians, by Elena Gambino (2000). For kids, retellings of Mesopotamian stories and lots of context.
Gods, Goddesses, and Monsters: An Encyclopedia of World Mythology, by Sheila Keenan (2000). Easy reading.
Gods, Demons and Symbols of Ancient Mesopotamia : An Illustrated Dictionary, by Jeremy Black and Anthony Green (1992).
Religion in Ancient Mesopotamia, by Jean Bottero (2001).